Going back to hemineglect: here are a couple good videos about it with some interviews of patients with the syndrome. The demonstration where the interviewer asks which finger he moves is remarkable. It is not as simple as a problem of vision, it's a problem of how the mind thinks about space.

The implications of this are very interesting: you do not see the world. You see a model of the world that your mind constructs, which, if constructed well, happens to be consistent with the world in order to allow you to understand and interact with it.

Fascinating! Another thing that I find intriguing is a condition where a person sees flashes of certain colors when listening to music. In the Foundation series, the Mule was thought to have this condition but he was able to transfer it to others when he composed his music.

Going back to hemineglect: here are a couple good videos about it with some interviews of patients with the syndrome. The demonstration where the interviewer asks which finger he moves is remarkable. It is not as simple as a problem of vision, it's a problem of how the mind thinks about space.

The implications of this are very interesting: you do not see the world. You see a model of the world that your mind constructs, which, if constructed well, happens to be consistent with the world in order to allow you to understand and interact with it.

Fascinating! Another thing that I find intriguing is a condition where a person sees flashes of certain colors when listening to music. In the Foundation series, the Mule was thought to have this condition but he was able to transfer it to others when he composed his music so they actually saw flashes of 3D art when listening to his music.

Yup, the best model indicates endless, accelerating expansion. How we know comes from a combination of theory and observations, which I'll briefly review.

The expansion of the universe is governed by general relativity, which describes how the contents of the universe affect the expansion rate, and the spatial curvature. The three big ingredients are matter, pressure, and a cosmological constant (AKA "dark energy"). "Dark matter" could be considered a fourth, but its effect is the same as regular matter so we don't bother distinguishing it for this purpose.

A higher density of matter causes the expansion rate to slow down, much like gravity slowing down a stone that was thrown upward. If the stone was not thrown fast enough, gravity wins and pulls it back. If a universe is filled with only matter, then following the Big Bang the expansion rate will decrease. If the matter density is high enough, then its gravitational field will slow the expansion to a halt and then pull the universe back together in a "Big Crunch".

Counter-intuitively, pressure (such as that produced by radiation and relativistic particles) also acts to slow the expansion rate. This is because the universe has no edges to push against. So instead of "pushing outward", the momentum of the particles providing the pressure acts as an additional source of gravitation, which is described through the stress-energy-momenta tensor. It also turns out that the effect of pressure decreases more quickly as the universe expands than does the effect of matter, and so it was most important in the early universe (the "radiation dominated era"), and is virtually negligible today.

Finally, there is dark energy, which can be thought of as a negative pressure that remains constant even as the universe expands. Negative pressure acts like an antigravity (more accurately it is best described as an intrinsic property of the space-time itself) and it makes the universe expand faster. This is pretty odd, but it is the most successful model for cosmology that we have (along with dark matter, forming the so-called "Lambda-CDM model", where lambda stands for dark energy and CDM stands for cold dark matter.) Dark energy also becomes more important over time, because its density remains constant while the density of matter decreases. So the universe proceeds from radiation dominated --> matter dominated --> dark energy dominated.

General relativity says that because the expansion of the universe is governed only by the density of these constituents, the fate of the universe is also intimately tied to them. "Density is destiny".

So to find out what model best describes the universe and its fate, we use observations to constrain what these densities are (relative to some "critical density" which would make the universe spatially flat), and check the expansion history. There are three independent techniques that help us do this:

-Type Ia Supernovae, which act as standard candles and give us a measure of the expansion history.-Cosmic Microwave Background (CMB), for which the angular size of the fluctuations reveal a lot about the universe's contents.-Galactic Clusters, which constrain the matter density (both regular and dark).

Plotting these data together, here is what we find. ΩMis the density of matter, and ΩΛ is the density of dark energy, in units of the critical density (ΩM + ΩΛ = 1)

The intersection of data show that the universe is very close to the critical density (which makes the geometry flat, such that parallel lines remain parallel and sum of angles in a triangle is 180°). About 30% of this density is in the form of matter, of which only 5% is accounted for by "regular" baryonic matter, and 25% is "dark matter". The remaining 70% is dark energy.

With the dark energy, the expansion is destined to continue forever, accelerating as it does (eventually it becomes an exponential as the universe is dark energy dominated). We can unambiguously reject the Big Crunch hypothesis, unless some dramatic new physics comes into play. Instead we (not really we, but our very distant descendants) are faced with "heat death" as the universe expands, entropy increases, and all structures eventually evaporate into radiation.

There is an open question regarding whether the expansion rate could increase so rapidly that all structures end getting torn apart -- this is the notorious "Big Rip" scenario. Whether or not the Big Rip occurs depends on what we call the "equation of state" of dark energy, characterized by a parameter "w". The Big Rip occurs if and only if w is less than -1, and the further below -1 it is, the sooner it happens.

For reasons of physics, the simplest model would have w be identical to -1, in which the Big Rip takes place infinitely far in the future. This is the boundary case between it occurring and never occurring.

Available data have this to say:

The intersection is consistent with w = -1, so we do not expect a Big Rip, but we also cannot rule it out. The best we can do is constrain how early it could happen, or by how much it can never happen, if that makes any sense.

I don't remember where I've read it, but I do remember that recent observations find out w being approximately equal to -1 but slightly less, this would not put the Big Rip infinitely far in the future but indeed very very far.

However, the lowest value you can see in the graph is -1.2 (I guess it's also the most unlikely), so, if Big Rip will ever happen, remaining time would be at least 439.651 billion years, that is still 31 times the current age of the universe. Quite a lot!

The universe is not required to be in perfect harmony with human ambition.

Each of the shaded regions represents sigma-confidence levels. The inner, darkest region is 1-sigma = 68% confidence that the true value does not lie outside that region, the next one is 2-sigma = 95% confidence it does not lie outside, and the outermost is 3-sigma = 99.7% confidence. The confidence levels also don't stop at 3-sigma -- they just don't show beyond there. You can probably guess from the widths where the 5th one would be, which is 99.99994%.

So by these data we can say we are more than 99% sure that w is within 0.2 of -1, for example.

There is definitely something deeply unsettling about the idea of all things being torn apart at the end of the universe, but on the other hand a heat death isn't really much better, nor is a Big Crunch. All spell certain doom to the universe's occupants who might somehow still be around, and none are clear insofar as whether they allow for the universe to continue with a chance of life afterward (even a Crunch does not necessarily imply a rebound, despite it being a popular idea).

There is definitely something deeply unsettling about the idea of all things being torn apart at the end of the universe, but on the other hand a heat death isn't really much better, nor is a Big Crunch.

Agreed, actually I'm very interested in the Baum-Frampton model (maybe I've already talked about this in a previous post), since the Big Rip has nothing to do with me whatsoever, would be a good thing if the Universe didn't "die" or end its life there, but start all over again.

Watsisname wrote:

All spell certain doom to the universe's occupants who might somehow still be around, and none are clear insofar as whether they allow for the universe to continue with a chance of life afterward (even a Crunch does not necessarily imply a rebound, despite it being a popular idea).

If it's possible to travel through multiverse (assuming it does exists) maybe it's possible to "escape" the Big Rip, but these occupants would survive in a sort of Limbo that (I think) also needs some energy to avoid collapsing. And... there would be no energy sources in such a place, so... yeah. A very interesting topic for a book though!

The universe is not required to be in perfect harmony with human ambition.

Well, if w does happen to be sufficiently far below -1, then the rip can happen well before all life is necessarily dead. Star formation does not end for about 100 trillion years, and the universe could still potentially support life until the evaporation of the largest supermassive black holes, which is about 10100 years. If w = -1.1 (which we can't rule out with better than 95% confidence) then the rip happens in about 100 billion years. Stars would still be shining.

But even so, I think "worry about it" isn't the right phrase, and I've never lost any sleep over thinking about it. We won't be around, and even if our descendants are they would be so different from us that it would be wrong to call them human. If we want to be worried about something there are numerous other possible dooms that can affect us directly.

I do think that end states are intellectually interesting, and can raise questions of physics and philosophy. They imply that not even a universe can forever support life, and the end states are the ultimate cosmic doom.